Question

if the cost of 10 greeting cards is equal to the selling price of 8 greeting cards find the gain or lose percent ​

Answer 1

Given :

• Cost of 10 greeting cards is equal to the selling price of 8 greeting cards.

To calculate:

• Gain or loss %

Calculation:

Let us first find the LCM of 10 and 8.

→ LCM of 10 and 8 = 2 × 5 × 2 × 2

→ LCM of 10 and 8 = 40

Now,

Let the CP of 10 greeting cards be Rs 40. Also,

Let the SP of the 8 greeting cards be Rs 40.

→ CP of 10 greeting cards = Rs 40

→ CP of 1 greeting card = Rs $\sf {\dfrac{40}{10} }$

→ CP of 1 greeting card = Rs 4

Also,

→ SP of 8 greeting cards = Rs 40

→ SP of 1 greeting card = Rs $\sf {\dfrac{40}{8} }$

→ SP of 1 greeting card = Rs 5

Here,

• Selling price > Cost price

So, here is profit.

→ Profit = SP - CP

→ Profit = Rs ( 5 - 4 )

→ Profit = Rs 1

Now, calculating profit %. As we know that,

★ $\boxed {\sf { Profit \: \% = \Bigg [\dfrac{Profit}{CP} \times 100 \Bigg ] \: \%}}$

Substituting values, we get :

→ $\sf { Profit \: \% = \Bigg [ \dfrac{1}{4} \times 100 \Bigg ] \%}$

→ $\sf { Profit \: \% = [ 1 \times 25 ] \%}$

→ $\boxed {\sf { Profit \: \% = 25 \%} }$ $\red{\bigstar}$

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$\small\boxed{ \begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Gain = S.P – C.P} \\ \\ \bigstar \:\sf{Loss = C.P – S.P} \\ \\ \bigstar \: \sf{Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{loss \: \% = \Bigg( \dfrac{loss}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{S.P = \dfrac{100+Gain\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100+Gain\%} \times S.P} \\ \\\bigstar \: \sf{ S.P = \dfrac{100-loss\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100-loss\%} \times S.P}\end{array} }$